An environmental agency monitors air quality at 8 different urban locations using two different portable sensors, Alpha (AAA) and Beta (BBB). The particulate matter readings (μg/m3\mu g/m^3μg/m3) recorded at the same time are shown in the table below:
| Location | L1 | L2 | L3 | L4 | L5 | L6 | L7 | L8 |
|---|---|---|---|---|---|---|---|---|
| Sensor Alpha (AAA) | 45 | 32 | 58 | 21 | 15 | 60 | 10 | 25 |
| Sensor Beta (BBB) | 40 | 35 | 50 | 28 | 12 | 65 | 18 | 22 |
Calculate Spearman's rank correlation coefficient for these data.
Test, at the 5% level of significance, whether there is a positive correlation between the readings of the two sensors. State your hypotheses clearly.
Sensor Beta was later found to have a calibration error at Location L2; the reading should have been 40 instead of 35.
Without performing any further calculations, explain the procedure for finding Spearman’s rank correlation coefficient given this change.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.